Start by bringing a large pot of salted water to a boil. While waiting, cut the broccoli into florets and discard the tough stem. Once the water is boiling, add the broccoli and cook for about 2-3 minutes until tender but still vibrant green. Remove the broccoli with a slotted spoon and set it aside.
In the same pot of boiling water, add the orecchiette pasta. Cook according to package instructions until al dente, usually about 9-11 minutes. Reserve about 1 cup of the pasta cooking water, then drain the pasta in a colander.
In a large skillet, heat the extra virgin olive oil over medium heat. Add the finely chopped shallots and sauté for about 2-3 minutes until they become translucent. Then, add the minced garlic and cook for an additional 30 seconds until fragrant.
Add the cooked orecchiette and broccoli to the skillet with the shallots and garlic. Toss everything together to combine. If the mixture seems dry, add a splash of the reserved pasta cooking water to help create a light sauce.
Season the pasta with salt, black pepper, and crushed red pepper flakes if you want a bit of heat. Stir in the freshly grated Parmesan cheese until it melts and coats the pasta. Taste and adjust seasoning as needed, then serve warm.
